What happens to sound at a surface. When sound meets the surface of a different material, its energy goes three ways: some is reflected back, some is absorbed (turned into heat in the material) and some is transmitted through. For a wall, R + A + T = 100%. Hard, dense materials such as concrete reflect nearly all of the sound. Soft, porous materials such as curtains and foam let the sound into their tiny gaps, where the moving air rubs against the fibres and turns the energy into heat: they absorb it.

Reflection. The angle of reflection equals the angle of incidence, both measured from the normal, the line at right angles to the surface.

Refraction. The speed of sound is different in different materials: 343 m/s in air, and about 3800 m/s in concrete and 1500 m/s in wood, but slower in porous materials (here, 320 m/s for the curtain and 220 m/s for the foam). The frequency stays the same, so the wavelength changes in proportion to the speed (λ = v/f). A wave front that meets the surface at an angle changes direction, by Snell’s law for waves:

sinθ₁ / v₁ = sinθ₂ / v₂, λ₂/λ₁ = v₂/v₁

Going into a slower material the sound bends towards the normal. Going into a faster material, such as air into concrete, it bends away from the normal, and beyond the critical angle sinθ_c = v₁/v₂ (5.2° for concrete, 13.2° for wood) there is no refracted wave and all of the sound is reflected. The sound that gets through the wall leaves from the other side at the original angle (the two faces of the wall are parallel), just as for a block of glass.

The energy values. The percentages are typical values for these materials at about 340 Hz, and the way they change with frequency is an illustration of two real trends: a heavy wall lets less low-pitched and even less high-pitched sound through (the “mass law”, transmission ∝ 1/f² here), and porous absorbers soak up high frequencies better than low ones. Real values depend on the thickness and on how the wall is mounted. Beyond the critical angle the model gives total reflection.

The pictures are slowed down a great deal (the real waves go about 130 times faster than the ones drawn), the wall is drawn much thicker than a real wall, and the crests show the wave fronts.